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I send photons one at a time through a Mach–Zehnder interferometer with two detectors. Quantum superposition ensures that photons only reach one of the detectors.

The interferometer is initially built on a frame. However, I can adjust it to allow the half-silvered mirrors to no longer be attached to each other by the frame, but move freely.

I perform the experiment with a single photon. One hour later, I measure the position of each mirror to determine if it was struck by the photon.

Does this minor change to the apparatus ensure that the superposition disappears and photons arrive at both detectors with equal probability?

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    $\begingroup$ Can you infer a photon's path by measuring the position of a mirror? If such a mirror exists, it would destroy superposition, IMO. $\endgroup$ – dominecf Dec 28 '20 at 10:50
  • $\begingroup$ For this question I'd like to keep it purely theoretical. Let's suppose we can measure the momentum transferred to the mirror when the photon is deflected by it, and we can do this a lengthy time after the detector registers $\endgroup$ – Peter A Dec 28 '20 at 11:26
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    $\begingroup$ I guess we are touching the very principe of quantum measurement. If the mirror recoils from the photon, the photon frequency changes... You know the story. No way around the uncertainty principle. $\endgroup$ – dominecf Dec 28 '20 at 11:31
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    $\begingroup$ Of course, photon-mirror recoil always exists. Supposing we can measure the momentum from the photon, we have to measure the momentum of the mirror before and after each H. O. M. interferometer run. No matter what technique we use, the extreme accuracy that is required will lead to randomization of the mirror position. $\endgroup$ – dominecf Dec 29 '20 at 20:14
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    $\begingroup$ Surprise surprise, if single photon path is to be detected from mirror $\Delta p$, the resulting mirror position inaccuracy $\Delta x$ will be comparable to photon wavelength. As an example, I suggest to measure the mirror position at different times with an interferometer - perhaps the most accurate technique ever; but even the interferometer shoots photons on the mirror, changing the momentum... $\endgroup$ – dominecf Dec 29 '20 at 20:17